Doctors treating Rep. Gabrielle Giffords on Monday said they removed several bone chips from the Tucson Democrat’s eye socket as she continues to recover from a gunshot wound to the head.

In a press conference with reporters, University Medical Center chief neurosurgeon Dr. Michael Lemole said Giffords’s eye sockets were fractured when she was injured. While the left side should heal, surgeons had to go in above Giffords’s right eyebrow, remove several fragments and then reconstruct her eye socket.

The surgery comes after doctors removed Giffords from a ventilator and inserted a breathing tube over the weekend. They are still watching to see how her speech will return, though she is currently unable to vocalize sounds because of the tube.

Still, Giffords’s husband, astronaut Mark Kelly, told ABC News’s Diane Sawyer that his wife is alert enough that she gave him a 10-minute back rub as he sat with her in her hospital room—a good sign, doctors said Monday.

“It does imply that she is recognizing him and that she is interacting with him perhaps in an old familiar way with him,” Lemole said. “All those higher, cognitive levels of function are at least somehow, somewhat preserved here.”

Lemole said that Giffords is doing as well Monday as she was before they performed the additional surgery to remove the bone chips in her eye. On Sunday, Giffords was upgraded from critical condition to serious condition.

Giffords and 12 others were wounded Saturday, Jan. 8, at a Safeway grocery store in north Tucson as she met with constituents. Six people were killed in the rampage. Charged in the shooting is 22-year-old Jared Lee Loughner, who is scheduled to appear in court Jan. 24.